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Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation LI Ping, LI Feng-jie Chinese Quarterly Journal of Mathematics    2024, 39 (4): 331-354.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.001 Abstract （205）      PDF（pc） （462KB）（109）       Knowledge map    Save This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian, which could be proposed as a model for the epitaxial growth of thin films. By using the variational method and the logarithmic type Sobolev inequality, we give some threshold results for blow-up solutions and global solutions, which could be classified by the initial energy. The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained. Related Articles | Metrics

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High Energy Normalized Solutions for the Schrödinger Equations with Exponential Critical Growth ZHANG Xiao-cang, XU Li-ping Chinese Quarterly Journal of Mathematics    2025, 40 (1): 1-19.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.001 Abstract （103）      PDF（pc） （417KB）（41）       Knowledge map    Save In this paper, we study high energy normalized solutions for the following Schrödinger equation …… Related Articles | Metrics

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Discontinuous Galerkin Method for Hydrodynamic and Sediment Transport Model ZHANG Ren-peng, WANG Bo, WANG Qiang, Chinese Quarterly Journal of Mathematics    2024, 39 (4): 355-365.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.002 Abstract （98）      PDF（pc） （1085KB）（67）       Knowledge map    Save In this article, we propose and research a first-order, linearized discontinuous Galerkin method for the approximation of the hydrodynamic and sediment transport model. The method is decoupled and fully discrete, and is shown to be unconditionally stable. Furthermore, error estimates are proved. Finally, the theoretical analysis is confirmed by numerical examples. Related Articles | Metrics

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The Hyers-Ulam Stability and Hyers-Ulam Instability for Some Nonhomogeneous Ordinary Differential Equations DENG Jing-tao Chinese Quarterly Journal of Mathematics    2024, 39 (4): 420-430.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.008 Abstract （77）      PDF（pc） （341KB）（48）       Knowledge map    Save In this paper, we get a necessary and sufficient condition such that a class of differential inequalities hold. Using this necessary and sufficient condition, we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability. And then, we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions. Related Articles | Metrics

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The Varieties of Semi-Conformal Vectors of Rank-One Even Lattice Vertex Operator Algebras CHU Yan-jun, GAO Yi-bo Chinese Quarterly Journal of Mathematics    2025, 40 (1): 36-48.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.004 Abstract （77）      PDF（pc） （430KB）（29）       Knowledge map    Save In this paper, we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors. We first give the varieties of semi-conformal vectors of a family of vertex operator algebras…… Related Articles | Metrics

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Fekete-Szegö Inequalities and the Symmetric Toeplitz Determinants for Certain Analytic Function Class Involving q-Differintegral Operator PEI Ke-ke, LONG Pin-hong, LIU Jin-lin, GANGADHARAN Murugusundaramoorthy Chinese Quarterly Journal of Mathematics    2024, 39 (4): 366-378.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.003 Abstract （69）      PDF（pc） （387KB）（80）       Knowledge map    Save In this paper, we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator. For this function class, we give the bound estimates of the coefficients a2 and a3 and some Fekete-Szegö functional inequalities. Besides, we also estimate the corresponding symmetric Toeplitz determinants. Furthermore, we point out some consequences and connections to these results above. Related Articles | Metrics

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Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral XIANG Chang-yong, DUAN Ji-song, LONG Qun-fei Chinese Quarterly Journal of Mathematics    2025, 40 (3): 304-312.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006 Abstract （64）      PDF（pc） （354KB）（25）       Knowledge map    Save We investigate the blow-up effect of solutions for a non-homogeneous wave equation utt −∆u−∆ut =I0α+ (|u|p)+ω(x), where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent. Related Articles | Metrics

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ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces LI Hong-feng, LIU Ke-feng, WANG Yong Chinese Quarterly Journal of Mathematics    2025, 40 (2): 111-134.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.001 Abstract （63）      PDF（pc） （367KB）（39）       Knowledge map    Save In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces. Related Articles | Metrics

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The w-(b,c)-Core Inverse FANG Li, ZHAO Liang Chinese Quarterly Journal of Mathematics    2025, 40 (1): 26-35.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.003 Abstract （55）      PDF（pc） （308KB）（44）       Knowledge map    Save We introduce and study a new kind of generalized inverses named w-(b,c)-core inverses, which is a generalization of the (b,c)-core inverse. An example is given to show that w-(b,c)-core inverses need not be (b,c)-core inverses. In addition, the dual version of the w-(b,c)-core inverse is studied. Some results on (b,c)-core inverses and e-(b,c)-core inverses are unified and generalized. Related Articles | Metrics

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A High-Order Scalar Auxiliary Variable Approach for Nonlinear Parabolic Integro-Differential Equations YAN Li-na, ZHANG Gen-gen, HUANG Qiong-ao Chinese Quarterly Journal of Mathematics    2025, 40 (3): 262-270.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.003 Abstract （55）      PDF（pc） （365KB）（3）       Knowledge map    Save An efficient and accurate scalar auxiliary variable (SAV) scheme for numerically solving nonlinear parabolic integro-differential equation (PIDE) is developed in this paper. The original equation is first transformed into an equivalent system, and the k-order backward differentiation formula (BDFk) and central difference formula are used to discretize the temporal and spatial derivatives, respectively. Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms, the proposed scheme is based on the SAV idea and can be treated semi-implicitly, taking into account both accuracy and effectiveness. Numerical results are presented to demonstrate the high-order convergence (up to fourth-order) of the developed schemes and it is computationally efficient in long-time computations. Related Articles | Metrics

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Branch and Bound Algorithm for Globally Solving Minimax Linear Fractional Programming WANG Hui-man, SHEN Pei-ping, LIANG Yu-xin Chinese Quarterly Journal of Mathematics    2024, 39 (4): 388-398.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.005 Abstract （48）      PDF（pc） （344KB）（22）       Knowledge map    Save In this paper, we study the minimax linear fractional programming problem on a non-empty bounded set, called problem (MLFP), and we design a branch and bound algorithm to find a globally optimal solution of (MLFP). Firstly, we convert the problem (MLFP) to a problem (EP2) that is equivalent to it. Secondly, by applying the convex relaxation technique to problem (EP2), a convex quadratic relaxation problem (CQRP) is obtained. Then, the overall framework of the algorithm is given and its convergence is proved, the worst-case iteration number is also estimated. Finally, experimental data are listed to illustrate the effectiveness of the algorithm. Related Articles | Metrics

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Novel Results on the Multi-Parameters Mittag-Leffler Function PAN Yu-mei, LI Yu-fen, CAI Dong-xin, YAN Xing-jie Chinese Quarterly Journal of Mathematics    2025, 40 (1): 82-92.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.008 Abstract （46）      PDF（pc） （328KB）（64）       Knowledge map    Save In this article, the multi-parameters Mittag-Leffler function is studied in detail. As a consequence, a series of novel results such as the integral representation, series representation and Mellin transform to the above function, are obtained. Especially, we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions. Meanwhile, some interesting integral operators and derivative operators of this function, are also discussed Related Articles | Metrics

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On α-Bloch Functions in Several Complex Variables ZHU Ting, YANG Liu Chinese Quarterly Journal of Mathematics    2025, 40 (1): 93-102.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.009 Abstract （44）      PDF（pc） （356KB）（14）       Knowledge map    Save In this paper, we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of Cm, which generalize and improve results of Aulaskari-Lappan, Minda, Aulaskari-Wulan, and Wu. Some examples are also given to complement our theory. Related Articles | Metrics

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A Note on a Result Due to Sauer and Schweizer WANG Guang-sheng, LI Fei, XU Yan Chinese Quarterly Journal of Mathematics    2025, 40 (1): 20-25.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.002 Abstract （43）      PDF（pc） （254KB）（15）       Knowledge map    Save n this paper, we obtain some normality criteria for families of meromorphic functions concering shared values, which extends the related results of Schwick, and SauerSchweizer, and can be viewed as a complement of the related results due to Pang-Zalcman, Xu-Fang. Related Articles | Metrics

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The Degree of Approximation by (E,q)(C,α,β) Means in Orlicz Spaces CHEN Lin, WU Ga-ridi Chinese Quarterly Journal of Mathematics    2024, 39 (4): 399-406.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.006 Abstract （43）      PDF（pc） （360KB）（16）       Knowledge map    Save In this paper, we study the trigonometric approximation problems of functions which belong to the Lipα class, the Lip(ξ(t)) class, and the W(L∗M;ξ(t)) class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces, the second mean value theorem for integrals, and (E,q)(C,α,β) means etc. At the same time, we give the corresponding degree of approximation. Related Articles | Metrics

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Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs JI Lin-xing, ZHANG Ke, HU Wen-jun Chinese Quarterly Journal of Mathematics    2024, 39 (4): 379-387.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.004 Abstract （43）      PDF（pc） （490KB）（131）       Knowledge map    Save Research on the independence polynomial of graphs has been very active. However, the computational complexity of determining independence polynomials for general graphs remains NP-hard. Let α(G) be the independence number of G and i(G; k) be the number of independent sets of order k in G, then the independence polynomial is defined as ...... Related Articles | Metrics

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On the Best Constant in Poincar´e Inequality over Simple Geometric Domains CHEN Hong-ru, MA Gao-chao, ZHANG Bei Chinese Quarterly Journal of Mathematics    2025, 40 (2): 148-157.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.003 Abstract （43）      PDF（pc） （410KB）（10）       Knowledge map    Save In this paper, we explicitly establish Poincar´e inequality for 1≤p <∞ over simple geometric domains, such as segment, rectangle, triangle or tetrahedron. We obtain sharper bounds of the constant in Poincar´e inequality and, in particular, the explicit relation between the constant and the geometric characters of the domain. Related Articles | Metrics

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A Spectral Radius Condition for a Graph to Have (a,b)-Parity Factors WANG Jun-jie, YU Yang, HU Jian-biao, WEN Peng Chinese Quarterly Journal of Mathematics    2024, 39 (4): 431-440.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.009 Abstract （40）      PDF（pc） （367KB）（40）       Knowledge map    Save Let a,b be two positive integers such that a≤b and a≡b (mod 2). We say that a graph G has an (a,b)-parity factor if G has a spanning subgraph F such that...... Related Articles | Metrics

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On Wiener Index of Power of Paths and Cycles LIU Sai-hua, LI Xiao-rong Chinese Quarterly Journal of Mathematics    2025, 40 (1): 49-58.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.005 Abstract （38）      PDF（pc） （328KB）（12）       Knowledge map    Save The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph. The kth power Gk of a graph G is the graph on V (G) and two vertices are adjacent if and only if their distance in G is less or equal to k. In this paper, we computed the Wiener index of the kth power of paths and cycles for any k ≥2. Related Articles | Metrics

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Power Options Pricing under Markov Regime-Switching Two-Factor Stochastic Volatility Jump-Diffusion Model 韩书书, 韦煜明 Chinese Quarterly Journal of Mathematics    2025, 40 (1): 59-73.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.006 Abstract （38）      PDF（pc） （558KB）（30）       Knowledge map    Save In this paper, we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options. Furthermore, we assume that the interest rates and the jump intensities of the assets are stochastic. Under the proposed framework, first, we derive the analytical pricing formula for power options by using Fourier transform technique, Esscher transform and characteristic function. Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation. Finally, we provide some sensitivity analysis of the model parameters to power options. Numerical examples show this model is suitable for empirical work in practice. Related Articles | Metrics